Electron affinities (EAs) of beryllium clusters are calculated up to the complete coupled-cluster single double triple (CCSDT) level using reasonably large basis sets with many diffuse functions. At all levels of theory, the obtained values for the adiabatic EA are large enough to be observed with standard photodetachment techniques. The vertical electron detachment energy is 0.341 eV for Be-2(-) and is 1.470 eV for Be-3(-) at the most precise CCSDT level. All studied beryllium anions are valence bound but the nature of binding is different in Be-2(-) and the two Be-3(-) isomers. The only factor of stabilization of the excess electron in Be-2(-) is the relaxation energy. Be-3(-)(D-infinityh) is stabilized by the relaxation energy and the Koopmans electrostatic and exchange energies; in Be-3(-)(D-3h), the main factors of stabilization are the correlation and relaxation energies. As was revealed in our study, in linear molecules the correlation contribution to the electron binding energy is negative, i.e., it decreases the EA.